On a modified version of the Lindley recursion

Dongzhou Huang ()
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Dongzhou Huang: Colorado State University

Queueing Systems: Theory and Applications, 2023, vol. 105, issue 3, No 4, 289 pages

Abstract: Abstract This paper concerns a modified version of the Lindley recursion, where the recursion equation is given by $$W_{i+1} = [V_{i} W_{i} + Y_{i}]^{+}$$ W i + 1 = [ V i W i + Y i ] + , with $$\{V_i\}_{i=0}^{\infty }$$ { V i } i = 0 ∞ and $$\{Y_i\}_{i=0}^{\infty }$$ { Y i } i = 0 ∞ being two independent sequences of i.i.d. random variables. Additionally, we assume that the $$V_i$$ V i take values in $$(-\infty , 1]$$ ( - ∞ , 1 ] and the $$Y_i$$ Y i have a rational Laplace–Stieltjes transform. Under these assumptions, we investigate the transient and steady-state behaviors of the process $$\{W_i\}_{i=0}^{\infty }$$ { W i } i = 0 ∞ by deriving an expression for the generating function of the Laplace–Stieltjes transform of the $$W_i$$ W i .

Keywords: Lindley recursion; Autoregressive models; Reflected process; Wiener–Hopf boundary value problem; Primary: 60K25; Secondary: 90B22 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11134-023-09886-8

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